Question

Find the term that must be added to the equation x2 + 10x= 5 to make it into a perfect square.

Answer 1

We always complete the square of a monic quadratic (coefficient on x² is one) by adding half the linear coefficient squared. Here that's half of 10, so 5, squared, so 25.

Answer: 25

x² + 10x = 5

x² + 10x + 25 = 5 + 25

(x + 5)² = 30

x + 5 = ±√30

x = -5 ±√30

Answer 2

25

Explanation:

x2 + 10x= 5

Take the coefficient of the x term

10

Divide it by 2

10/2 =5

Square it

5^2=25

Add this to both sides